Question 617662: Can you please help me in answering the following:
(A) Find the binomial probability P(x = 5), where n = 12 and p = 0.70.
(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A) Find the binomial probability P(x=5), where (n=13) and p=0.70.
P(x=5) = 13C5(0.7)^5*0.3^8 = 0.0142
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B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
P(x >= 5) = 1 - P(0<= x <=4) = 1-0.0034 = 0.9966
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C) How would you find the normal approximation to the binomial probability
P(x=5) in part A? Please show how you would caculate u and o in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the caculations.
u = np = 13*0.7 = 9.1
sigma = sqrt(npq) = sqrt(9.1*0.3) = 1.6523
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Switching from Binomial to Normal:
P(x = 5) = P(4.5 <= x <= 5.5)
z(4.5) = (4.5-9.1)/1.6523 = -2.7840
z(5.5) = (5.5-9.1)/1.6523 = -2.1788
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P(4.5 <= x <= 5.5) = P(-2.7840<= z <= -2.1788) = 0.0120
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Cheers,
Stan H.
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